The ratio of boys to girls in a school is 5:8. If the number
of girls exceeds the number of boys by 144, calculate the
total number of students in the school.​

Answer: The expression (equation/formula) for the volume of a:  

     " right rectangular prism " ;   is represented by:

____________________________________________________

                    →   " V  =  L * w * h  "   ;

____________________________________________________

in which:   all the dimensions are in the same "units of measurement" (or converted to the same "units of measurement" ;  

and in which:

      " V " is the "volume" of the right rectangular prism; in the "cubic units" ; or written as:  "units³ "  ;  or, [insert the particular units used}^ ³  "   ;

  →  that is, [units] raised to the "3rd [third] power" ; assuming these units are the same  same "fundamental units of measurement"  as the "other 2 (two) values in the expression".  

    If we are given no specific units of measurement whatsoever, then we use the generic term, "units" as the "units of measurement" ; and we express the "volume; "V" ;  of a "right rectangular prism" as:  " units ³ " ; or "cubic units" ;

        in our answer— if we are asked to solve for the:

                     "volume; "V";  of a "right rectangular prism" ;

_________________________________________________

and in which:  

            "L" represents the "length" of a "right rectangular prism" ;

            "w" represents the "width" of a "right rectangular prism" ;

            "h" represents the "height" of a "right rectangular prism" .

_________________________________________________

To given an example:

  Say we have a "right rectangular prism" ; with the given measurements:

    width , "w" :   w = 2 units;  

    length, "L"  :    L  = 3 units ;

    height, "h" :    h =  8 units.

_________________________________________________

We are asked to "find the volume " ;  of this "right recentangular prism" .

The formula for the volume;  "V" ;  of this "right rectangular prism" ;

is:

_________________________________________________

          →    Volume  =  Length * width * height ;

that is:

          →    V =  L  * w * h  ;  

Solve for the volume;  "V" .

_________________________________________________

          →   V  =  L  * w * h   ;    Now plug in the values given:

          →   V =  (3 units)  * (2 units)  * (8 units) ;

                    =  3 * 2 * 8 * (units) * (units) * (units) ;

                    =  3 * 2 * 8 * units ³  ;

                    =  48 units ³ .    

_________________________________________________                    

Hope this answer— and explanation—is helpful to you!

     Wishing you the best in your academic pursuits

               — and within the "Brainly" community!

_________________________________________________

Answer: A

Step-by-step explanation:

Answer:

The correct answer is option D. (3h + 7)(h – 6)

Step-by-step explanation:

It is given a quadratic function ,

3h² - 11h - 42

To find the factors of given function

3h² - 11h - 42  = 3h² - 18h  + 7h - 42

 = 3h(h -6) + 7(h - 6)

 =(h - 6)(3h + 7)

 = (3h + 7)(h – 6)

The correct answer is option D. (3h + 7)(h – 6)

Answer:

See attachment

The relation is not a function.

The domain is [-4.1,3.9]

The range is [-2.1,5.9]

Step-by-step explanation:

The given relation has ordered pairs (3.9, 5.9), (–1.1, 5.9), (–4.1, 3.9), (–4.1, –2.1)

It is implied in the ordered pairs that the relation is a continuous function.

We plot the points and connect them with straight lines as shown in the attachment.

The relation is not a function because its graph fails the vertical line test.

In other words, we have an x-coordinate that corresponds to more than one y-coordinate.

-4.1 corresponding to 3.9 and -2.1 at the same time.

The domain is the set of values for which the function is defined.

The domain is [-4.1,3.9]

The range refers to the corresponding y-values for which the function exists.

The range is [-2.1,5.9]

Answer:

x = 1.47  or x = -7.47

Step-by-step explanation:

x²+6x+9=20

This is a quadratic equation

x²+6x+9-20=0

x²+6x-11=0

Step 1 : Write the quadratic formula

x = -b±√b²-4(a)(c)

              2a

Step 2 : Substitute values in the formula

a = 1

b = 6

c = -11

x = -6±√6²-4(1)(-11)

              2(1)

x = -6±√80

          2

x = -3 + 2√5 or x = -3 - 2√5

x = 1.47         or x = -7.47

!!

Answer:

x=1.472 or x=-7.472

Step-by-step explanation:

Lets begin by rearranging the equation into the format ax²+bx+c=0

The equation will be:

x²+6x+9-20=0

x²+6x-11=0

We shall use the quadratic formula to solve the equation.

x=[-b±√(b²-4ac)]/2a

=[-6±√(6²-4×1×-11)]/2

=[-6±√80]/2

=[-6±8.944]2

x= Either (-6+8.944)/2 or x= (-6-8.944)/2

Solving for x in each case gives:

x=1.472 or x=-7.472

Answer:

Step-by-step explanation:

The point-slope of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-2, 0) and (2, 8).

Substitute:

[tex]m=\dfrac{8-0}{2-(-2)}=\dfrac{8}{4}=2[/tex]

for the point (-2, 0):

[tex]y-0=2(x-(-2))\\\\y-0=2(x+2)[/tex]

for the point (2, 8):

[tex]y-8=2(x-2)[/tex]

Answer:

y-4 =-1(x+1)  point slope form

y-2 = -1(x-1)

y = -x +3  slope intercept form

Step-by-step explanation:

We have 2 points, we can find the slope

m = (y2-y1)/(x2-x1)

   = (2-4)/(1--1)

   (2-4)/(1+1)

     -2/2

   =-1

The slope is -1

Then we can use point slope form to find an equation

y-y1 =m(x-x1)

y-4 = -1(x--1)

y-4 =-1(x+1)  point slope form

Using the other point

y-2 = -1(x-1)

Distribute the -1

y-2 = -1x +1

Add 2 to each side

y-2+2 = -x+1+2

y = -x +3  slope intercept form

Answer: C. 96%  --------  APEX :D

Answer:

B) 46.67°

Step-by-step explanation:

Step 1 : Write the cosine formula to find the angle C

c² = a² + b² - 2ab cos C

Step 2 : Substitute the values in the formula

6² = 7² + 8² - 2(8)(7) cos C

cos C = 0.6875

C = cos^-1 (0.6875)

C = 46.567 °

Step 3 : Round off to 2 decimal places

Angle C = 46.57°

!!

Well,

Given that [tex]x=\sin(\theta)[/tex],

We can rewrite the equation like,

[tex]\dfrac{\sin(\theta)}{\sqrt{1-\sin(\theta)^2}}[/tex]

Now use, [tex]\cos(\theta)^2+\sin(\theta)^2=1[/tex] which implies that [tex]1-\sin(\theta)^2=\cos(\theta)^2[/tex]

That means that,

[tex]\dfrac{\sin(\theta)}{\sqrt{1-\sin(\theta)^2}}\Longleftrightarrow\dfrac{\sin(\theta)}{\sqrt{\cos(\theta)^2}}[/tex]

By def [tex]\sqrt{x^2}=x[/tex] therefore [tex]\sqrt{\cos(\theta)^2}=\cos(\theta)[/tex]

So the fraction now looks like,

[tex]\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]

Which is equal to the identity,

[tex]\boxed{\tan(\theta)}=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]

Hope this helps.

r3t40

Answer:

Part 1) The length of the diagonal of the outside square is 9.9 units

Part 2) The length of the diagonal of the inside square is 7.1 units

Step-by-step explanation:

step 1

Find the length of the outside square

Let

x -----> the length of the outside square

c ----> the length of the inside square

we know that

[tex]x=a+b=4+3=7\ units[/tex]

step 2

Find the length of the inside square

Applying the Pythagoras Theorem

[tex]c^{2}= a^{2}+b^{2}[/tex]

substitute

[tex]c^{2}= 4^{2}+3^{2}[/tex]

[tex]c^{2}=25[/tex]

[tex]c=5\ units[/tex]

step 3

Find the length of the diagonal of the outside square

To find the diagonal Apply the Pythagoras Theorem

Let

D -----> the length of the diagonal of the outside square

[tex]D^{2}= x^{2}+x^{2}[/tex]

[tex]D^{2}= 7^{2}+7^{2}[/tex]

[tex]D^{2}=98[/tex]

[tex]D=9.9\ units[/tex]

step 4

Find the length of the diagonal of the inside square

To find the diagonal Apply the Pythagoras Theorem

Let

d -----> the length of the diagonal of the inside square

[tex]d^{2}= c^{2}+c^{2}[/tex]

[tex]d^{2}= 5^{2}+5^{2}[/tex]

[tex]d^{2}=50[/tex]

[tex]d=7.1\ units[/tex]

If a = 4 units and b = 3 units, the length of the diagonal of the outside square rounded to the nearest tenth is  9.9 units

units and the length of the diagonal of the inside square rounded to the nearest tenth is 7.1 units

Let's solve its step by step

step 1

Find the length of the outside square

Let

x -----> the length of the outside square

c ----> the length of the inside square

we know that

x=a+b=4+3=7 units

step 2

Find the length of the inside square

Applying the Pythagoras Theorem

[tex]c^(2)= a^(2)+b^(2)[/tex]

substitute

[tex]c^(2)= 4^(2)+3^(2)[/tex]

[tex]c^(2)=25[/tex]

c=5 units

step 3

Find the length of the diagonal of the outside square

To find the diagonal Apply the Pythagoras Theorem

Let

D -----> the length of the diagonal of the outside square

[tex]D^(2)= x^(2)+x^(2)[/tex]

[tex]D^(2)= 7^(2)+7^(2)[/tex]

[tex]D^(2)=98[/tex]

D=9.9 units

step 4

Find the length of the diagonal of the inside square

To find the diagonal Apply the Pythagoras Theorem

Let

d -----> the length of the diagonal of the inside square

[tex]d^(2)= c^(2)+c^(2)[/tex]

[tex]d^(2)= 5^(2)+5^(2)[/tex]

[tex]d^(2)=50[/tex]

d=7.1 units

Answer:

x=2, y=7 -------> y=11-2x  and 4x-3y=-13

x=5, y=2 ------> 2x+y=12 and x=9-2y

x=3, y=5  -----> 2x+y=11 and x-2y=-7

x=7, y=3 ------> x+3y=16  and  2x-y=11

Step-by-step explanation:

Part 1) we have

2x+y=12 -----> equation A

x=9-2y -----> equation B

Solve by substitution

Substitute equation B in equation A and solve for y

2(9-2y)+y=12

18-4y+y=12

4y-y=18-12

3y=6

y=2

Find the value of x

x=9-2(2)=5

therefore

The solution is

x=5, y=2

Part 2) we have

x+2y=9 -----> equation A

2x+4y=20 ---> equation B

Multiply equation A by 2 both sides

2(x+2y)=9*2

2x+4y=18 -----> equation C

Compare equation C with equation B

Both equations have the same slope with different y-intercept

therefore

The lines are parallel and the system has no solution

Part 3) we have

x+3y=16 ------> equation A

2x-y=11 -----> equation B

Solve the system by elimination

Multiply equation B by 3 both sides

3(2x-y)=11*3

6x-3y=33 -----> equation C

Adds equation A and equation C

x+3y=16

6x-3y=33

----------------

x+6x=16+33

7x=49

x=7

Find the value of y

x+3y=16

7+3y=16

3y=16-7

3y=9

y=3

therefore

The solution is

x=7, y=3

Part 4) we have

y=11-2x -----> equation A

4x-3y=-13 ---> equation B

Solve by substitution

Substitute equation A in equation B and solve for x

4x-3(11-2x)=-13

4x-33+6x=-13

10x=-13+33

10x=20

x=2

Find the value of y

y=11-2(2)=7

therefore

The solution is

x=2, y=7

Part 5) we have

y=10+x -----> equation A

-3x+3y=30 ---> equation B

Multiply equation A by 3 both sides

3*y=3*(10+x)

3y=30+3x

Rewrite

-3x+3y=30 ----> equation C

equation B and equation C are identical

therefore

The system has infinitely solutions

Part 6) we have

2x+y=11 -----> equation A

x-2y=-7 ----> equation B

Solve by elimination

Multiply equation A by 2 both sides

2(2x+y)=11*2

4x+2y=22 ----> equation C

Adds equation B and equation C and solve for x

x-2y=-7

4x+2y=22

----------------

x+4x=-7+22

5x=15

x=3

Find the value of y

x-2y=-7

3-2y=-7

2y=3+7

2y=10

y=5

therefore

The solution is

x=3, y=5  

The situation "The time it takes to read a book depends on the number of pages in the book" in function notation is: A. Time(pages).

In Mathematics, a function is typically used in mathematics for uniquely mapping an input variable (domain or independent value) to an output variable (range or dependent value).

This ultimately implies that, an independent value represents the value on the x-axis of a cartesian coordinate while a dependent value represents the value on the y-axis of a cartesian coordinate.

In this context, we can logically deduce that time is a function of the number of pages, so it should be written in function notation as follows:

Time(pages).

Complete Question:

Which of the following shows the situation below in function notation?

The time it takes to read a book depends on the number of

pages in the book.

A. Time(pages)

B. Book(pages)

C.Pages(time)

D. Book(time)

Answer:

[tex]\log_{144}(12)=\frac{1}{2}[/tex]

Step-by-step explanation:

First step identify the base.  The base is 144.

The exponent is the logarithm.

The number not mentioned is the one that goes inside.

In other words [tex]a^x=b[/tex] is equivalent to [tex]log_a(b)=x[/tex]

There are some restrictions on what a and b can be.

You read  [tex]log_a(b)=x[/tex] as log base a of b equals x

x is the exponent

a is the base

So we have log base 144 of 12 equals 1/2

[tex]\log_{144}(12)=\frac{1}{2}[/tex]

Answer:

it would be the 4th option

Step-by-step explanation:

all the above are wrong except the fourth option because a 3-D square or cube is made up of 6 equal squares. I hope this helps a-lot. : )

The 3-D figure Scarlett can make and the combinations of shapes she can use is a square prism with six squares.

A square prism is a three-dimensional object that is made up of six squares.

The volume of a square prism = length x width x height.

To learn more about right square prism, please check: https://brainly.com/question/13048128

Answer:

The shortest distance from A to C is [tex]AC=5\sqrt{13}\ units[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The shortest distance from A to C is the hypotenuse of the right triangle AYC

Applying the Pythagoras Theorem

[tex]AC^{2}=AY^{2} +YC^{2}[/tex]

step 1

Find the length YC (hypotenuse of the right triangle YBC)

Applying the Pythagoras Theorem

[tex]YC^{2}=YB^{2} +BC^{2}[/tex]

substitute the given values

[tex]YC^{2}=6^{2} +15^{2}[/tex]

[tex]YC^{2}=261[/tex]

[tex]YC=\sqrt{261}\ units[/tex]

step 2

Find the shortest distance from A to C

[tex]AC^{2}=AY^{2} +YC^{2}[/tex]

substitute the given values

[tex]AC^{2}=8^{2} +\sqrt{261}^{2}[/tex]

[tex]AC^{2}=325[/tex]

[tex]AC=\sqrt{325}\ units[/tex]

[tex]AC=5\sqrt{13}\ units[/tex]

Answer:

3

Step-by-step explanation:

g(-1) means what is g(x) when x=-1.

So find -1 under the column labeled x and then scroll directly to the right of that and you should see what g(-1).  It is 3

Here are my examples:

g(-8)=6

g(-5)=-2

g(-1)=3

g(0)=-5

Answer:

[tex]\large\boxed{y-4=\dfrac{1}{2}(x+2)\text{- point-slope form}}\\\boxed{y=\dfrac{1}{2}x+5\text{- slope-intercept form}}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have the slope [tex]m=\dfrac{1}{2}[/tex] and the point [tex](-2, 4)[/tex].

Substitute:

[tex]y-4=\dfrac{1}{2}(x-(-2))[/tex]

[tex]y-4=\dfrac{1}{2}(x+2)[/tex] - point-slope form

Convert to the slope-intercept form (y = mx + b):

[tex]y-4=\dfrac{1}{2}(x+2)[/tex]         use the distributive property

[tex]y-4=\dfrac{1}{2}x+1[/tex]         add 4 to both sides

[tex]y=\dfrac{1}{2}x+5[/tex] - slope-intercept form

[tex]\left(1-\dfrac{2}{3}\right)\cdot\dfrac{6}{9}=\dfrac{1}{3}\cdot \dfrac{2}{3}=\dfrac{2}{9}[/tex]

The pharmacist has 2 more prescriptions left to review that you filled.

To find out how many prescriptions the pharmacist has left to review, we can follow these steps:

1. Calculate the total number of prescriptions filled by you:

[tex]\[ \text{Total filled prescriptions} = \frac{6}{9} \times \text{Total prescriptions} \][/tex]

2. Calculate the number of prescriptions reviewed by the pharmacist:

[tex]\[ \text{Prescriptions reviewed by pharmacist} = \frac{2}{3} \times \text{Total filled prescriptions} \][/tex]

3. Calculate the number of prescriptions left for the pharmacist to review:

[tex]\[ \text{Prescriptions left to review} = \text{Total filled prescriptions} - \text{Prescriptions reviewed by pharmacist} \][/tex]

Let's put the numbers into these equations. Assuming there were initially 9 prescriptions:

1. Total filled prescriptions:

[tex]\[ \text{Total filled prescriptions} = \frac{6}{9} \times 9 = 6 \][/tex]

2. Prescriptions reviewed by pharmacist:

[tex]\[ \text{Prescriptions reviewed by pharmacist} = \frac{2}{3} \times 6 = 4 \][/tex]

3. Prescriptions left to review:

[tex]\[ \text{Prescriptions left to review} = 6 - 4 = 2 \][/tex]

Answer:

The farmers will have the same amount of feed (300 lbs) in 3 days

Step-by-step explanation:

After dividing the total amounts of feed by the daily feed amounts, it’s found that the two farmers will have the same amount of feed left after approximately 3.5 days.

To solve this problem, you need to find out how many days it takes for both farmers to run out of feed. For the first farmer, divide the total amount of feed (700 pounds) by the amount he uses each day (200 pounds). This comes to 3.5 days. For the second farmer, divide his total feed (1000 pounds) by the amount he uses each day (350 pounds), which comes to approximately 2.857 days.

Since we want to know when they will have the same amount of feed left, we look for the higher number, because the first farmer will still have feed left when the second farmer runs out. Therefore, the two farmers will have the same amount of feed left after around 3.5 days.

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Answer:

Step-by-step explanation:

A will.

Suppose the object is placed on (5,4)

If you rotate it 180o counterclockwise, the point will become (-5,-4) (both x and y will change signs.)

Moving one unit down will still leave you in quadrant III.

If you start in another quadrant, this answer will not be correct. If the point started out in quadrant 2, rotating it 180o counterclockwise will put you in quad 4. For example

Object Start: (-2,3)    Starts in quad 2

Image found: (- -2, - 3) = (2, - 3) which is in quad 4.

Answer:

[tex]\boxed{\text{0.675 h}}[/tex]

Step-by-step explanation:

18 min = 0.3 h

Car 1 started 0.3 h before Car 2.

  Let t = time of Car 2. Then

t + 0.3 = time of Car 1

Distance = speed × time, and both cars travel the same distance. Then

[tex]\begin{array}{rcl}45(t + 0.3) & = & 65t\\45t + 13.5 & = & 65t\\20t & = & 13.5\\t & = & \textbf{0.675 h}\\\end{array}\\\text{Car will overtake Car 1 in } \boxed{\textbf{0.675 h}}[/tex]

Check:

[tex]\begin{array}{rcl}45(0.675 + 0.3) & = & 65 \times 0.675\\45 \times 0.975 & = & 43.875\\43.875 & = & 43.875\\\end{array}[/tex]

OK.

Answer:

Car2 overtakes Car1 after 0.675 hours

Step-by-step explanation:

To solve this question, we must know that

Speed = distance / time

Speed_car1 = 45 mph = distance_car1/ time_1

Speed_car2= 65 mph = distance_car2/ time_2

We know that

time1 - time2 = 18 minutes = 0.3 h

And, at the time of the overtake, both cars will have traveled the same distance.

So,

distance_car1 = 45 mph * time1 = distance_car2 = 65 mph * time2

time1 / time2 = 65/45

time1 = 1.444*time2

Then,

1.444*time2- time2 =  0.3 h

time2 = 0.675 h

time1 = 0.975 h

Car2 overtakes Car1 after 0.675 hours

Answer: H. 35 games

Step-by-step explanation: Set up a proportion.

5/8 = X/56

Cross multiply.

5 x 56 = 280

8 x X = 8x

The cross multiplied equation will be 280=8x.

Divide by 8 in order to isolate x.

x=35

They will win 35 games.

Answer:

The answer is H. 35 games

Answer:

[tex]96x^4y+104x^2y^2[/tex]

is the simplified form of

your given problem:

[tex](12x^2+13y)(4x \times 2xy)[/tex].

Step-by-step explanation:

So the given problem is this:

[tex](12x^2+13y)(4x \times 2xy)[/tex]

I'm going to do the multiplication in the second ( ).

Nothing can be done in the first ( ) because the operation is addition and those two terms aren't like terms.

[tex](12x^2+13y)(8x^2y)[/tex]

I got x^2 because of x(x) part.

Now we get to distribute 8x^2y to both terms in the ( ).

[tex]12x^2 \cdot 8x^2y+13y \cdot 8x^2y[/tex]

Adding exponents on bases that have the same variable:

[tex]96x^4y+104x^2y^2[/tex]

Answer:

x = -16

Step-by-step explanation:

  3          

 (— • x) -  -24  = 0  

  2        

       -24     -24 • 2

   -24 =  ———  =  ———————

           1         2  

For this case we must solve the following equation:

[tex]\frac {3} {- 2x} = 24[/tex]

Multiplying by 2x on both sides of the equation:

[tex]-3 = 24 * 2x\\-3 = 48x[/tex]

Dividing between 48 on both sides of the equation:

[tex]x = - \frac {3} {48}[/tex]

We simplify:

[tex]x = - \frac {1} {16}[/tex]

Answer:[tex]x = - \frac {1} {16}[/tex]

Answer:

B. 40

Step-by-step explanation:

All triangle angles equal 180

100+40=140

180-140=40

B. 40 is the answer.

Answer:

(5, 9)

Step-by-step explanation:

Given the 2 equations

x = 5 → (1)

y = 2x - 1 → (2)

x = 5 is the value of the x- coordinate.

Substitute x = 5 into (2) for the corresponding value of y

y = (2 × 5) - 1 = 10 - 1 = 9

Solution is (5, 9 )

Answer:

1380 meters

Step-by-step explanation:

perimeter of a rectangle :2(l+b)

2(150 +80)

2(230)

460 meters of wire for one round

for three rounds :3×460=

1380 meters

Answer:

x < 3/2.

Step-by-step explanation:

1/3( 5x + 3) < 1/4(6x + 5)

5/3 x + 1 < 3/2x + 5/4

5/3 x - 3/2 x < 5/4 - 1

1/6 x < 1/4

x < 6/4

x < 3/2.

The value of the variable x is less than 3/2.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Let x be the number.

One-third of the sum of 5 times a number and 3 is less than one-fourth the sum of six times that number and 5. Then the equation will be

(1/3)(5x + 3) < (1/4)(6x + 5)

Simplify the inequality, then the value of x will be

20x + 12 < 18x + 15

2x < 3

x < 3/2

The value of the variable x is less than 3/2.

More about the solution of the equation link is given below.

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#SPJ2

Final answer:

The vertex of a parabola in the form y = ax + bx² can be found using the vertex formula x = -b/(2a). The vertex represents the highest or lowest point on the graph depending on whether a is positive or negative.

Explanation:

The vertex of a parabola in the form y = ax + bx² can be found using the vertex formula. The vertex formula is x = -b/(2a), which gives the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute the x-coordinate into the equation y = ax + bx². The vertex of the parabola represents the highest or lowest point on the graph, depending on whether the coefficient a is positive or negative.